Petrie multiplier¶
A composition model in which equal individual rates of cross-group remarks yield unequal expected recipient exposure, amplified by the squared size ratio under its basic random-targeting assumptions.
Core Idea¶
The Petrie multiplier separates behavior rates from exposure rates. Each member of two groups is assigned the same propensity to direct a remark at the other group. When one group is much larger, its many potential sources concentrate events among fewer opposite-group recipients, while the minority group's events are diluted among many recipients.
The square-law comparison follows from the basic counting assumptions, not from a universal law of social behavior. Heterogeneous rates, repeated contacts, network structure, nonbinary grouping, and nonrandom targeting require extensions. The model is a thought experiment until its variables and assumptions are empirically measured.
Scope of Application¶
- Workplace composition. Illustrates why minority experience can differ from majority impressions.
- Exposure modeling. Distinguishes event production from per-recipient burden.
- Diversity analysis. Generates testable hypotheses about composition and reported experience.
- Simulation. Explores departures from equal rates and random targeting.
- Statistical communication. Demonstrates denominator effects without inferring individual intent.
Clarity¶
State group definitions and sizes, event type, per-person source-rate assumption, target-selection rule, observation period, and whether results are expectations, simulations, or measured data. Avoid binary-gender generalization and causal conclusions not supported by the model. Inclusion test: Require two group sizes, equal per-person source propensity, cross-group events, random or specified target allocation, and comparison of expected received events per member. Exclusion test: Exclude an empirical prevalence estimate, proof that the two groups behave equally, causal attribution of any observed disparity, and applications where targeting is within-group or network-structured without revising the model. Nearest boundary: The model explains a composition-induced exposure asymmetry under equal propensity; it does not claim equal actual behavior or measure discrimination in a real setting without data. Exit condition: The identity changes when event rates, target choice, or group structure are altered without deriving the corresponding new expectation. Common misclassifications: It is not evidence that actual groups offend at equal rates. It is not an empirical estimate of experienced sexism. It is not a generic multiplier effect. It is not valid unchanged for networked or within-group targeting. Nearest named distinctions: Lanchester Square Law: Lanchester models combat attrition; the Petrie model uses analogous square scaling for directional exposure under different assumptions. Risk Ratio: A risk ratio compares observed probabilities, whereas the multiplier derives expected exposure from a stylized mechanism. Ecological Fallacy: The model operates on group expectations and cannot determine any individual's behavior or experience. Multiplier Effect: Generic amplification mechanisms do not specify this two-group source–target denominator structure.
Manages Complexity¶
The multiplier compresses a directional interaction system into sources, targets, rates, and group sizes. It exposes how identical actor propensities can generate unequal recipient burdens and identifies exactly which structural and behavioral assumptions must be tested rather than argued from intuition.
Abstract Reasoning¶
- Define the two groups and count members.
- Specify the cross-group event and equal or unequal source rates.
- Declare how targets are selected.
- Compute total events from each source group.
- Divide by the number of recipients in the opposite group and compare expectations.
- Stress-test heterogeneity, networks, uncertainty, and empirical fit.
Knowledge Transfer¶
The transferable cargo is directional exposure accounting in an imbalanced bipartite population. It transfers to other interaction harms or benefits only with equivalent source, target, and allocation rules; it stops at rhetorical use of square law without a model.
Relationships to Other Abstractions¶
Current abstraction Petrie multiplier Domain-specific
Parents (1) — more general patterns this builds on
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Petrie multiplier is a kind of Formal Model Domain-specific
The Petrie multiplier is a formal probabilistic composition model relating group proportions, equal individual remark rates, and unequal expected recipient exposure.
Hierarchy path (1) — routes to 1 parentless root
- Petrie multiplier → Formal Model → Representation → Abstraction
Neighborhood in Abstraction Space¶
Petrie multiplier sits in a moderately populated region (45th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Social Structure & Group Identity (12 abstractions)
Nearest neighbors
- Precision marketing — 0.87
- Kruskal–Wallis Test — 0.87
- N-of-1 Trial — 0.87
- Lincoln Index — 0.86
- Optimal Distinctiveness Theory — 0.86
Computed from structural-signature embeddings · 2026-10-08